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Theoretical Biology and Medical Modelling This Provisional PDF corresponds to the article as it appeared upon acceptance Fully formatted PDF and full text (HTML) versions will be made available soon Time series analysis as input for clinical predictive modeling: Modeling cardiac arrest in a pediatric ICU Theoretical Biology and Medical Modelling 2011, 8:40 doi:10.1186/1742-4682-8-40 Curtis E Kennedy (cekenned@texaschildrenshospital.org) James P Turley (James.P.Turley@uth.tmc.edu) ISSN Article type 1742-4682 Research Submission date 22 November 2010 Acceptance date 24 October 2011 Publication date 24 October 2011 Article URL http://www.tbiomed.com/content/8/1/40 This peer-reviewed article was published immediately upon acceptance It can be downloaded, printed and distributed freely for any purposes (see copyright notice below) Articles in TBioMed are listed in PubMed and archived at PubMed Central For information about publishing your research in TBioMed or any BioMed Central journal, go to http://www.tbiomed.com/authors/instructions/ For information about other BioMed Central publications go to http://www.biomedcentral.com/ © 2011 Kennedy and Turley ; licensee BioMed Central Ltd This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited Time series analysis as input for clinical predictive modeling: Modeling cardiac arrest in a pediatric ICU Curtis E Kennedy1§, James P Turley2 Department of Pediatrics, Baylor College of Medicine, 6621 Fannin, WT 6-006, Houston, TX 77030, USA The University of Texas School of Biomedical Informatics, 7000 Fannin, Suite 600, Houston, TX 77030, USA § Corresponding Author Email addresses: CEK: cekenned@texaschildrenshospital.org JPT: James.P.Turley@uth.tmc.edu Abstract Background: Thousands of children experience cardiac arrest events every year in pediatric intensive care units Most of these children die Cardiac arrest prediction tools are used as part of medical emergency team evaluations to identify patients in standard hospital beds that are at high risk for cardiac arrest There are no models to predict cardiac arrest in pediatric intensive care units though, where the risk of an arrest is 10 times higher than for standard hospital beds Current tools are based on a multivariable approach that does not characterize deterioration, which often precedes cardiac arrests Characterizing deterioration requires a time series approach The purpose of this study is to propose a method that will allow for time series data to be used in clinical prediction models Successful implementation of these methods has the potential to bring arrest prediction to the pediatric intensive care environment, possibly allowing for interventions that can save lives and prevent disabilities Methods: We reviewed prediction models from nonclinical domains that employ time series data, and identified the steps that are necessary for building predictive models using time series clinical data We illustrate the method by applying it to the specific case of building a predictive model for cardiac arrest in a pediatric intensive care unit Results: Time course analysis studies from genomic analysis provided a modeling template that was compatible with the steps required to develop a model from clinical time series data The steps include: 1) selecting candidate variables; 2) specifying measurement parameters; 3) defining data format; 4) defining time window duration and resolution; 5) calculating latent variables for candidate variables not directly measured; 6) calculating time series features as latent variables; 7) creating data subsets to measure model performance effects attributable to various classes of candidate variables; 8) reducing the number of candidate features; 9) training models for various data subsets; and 10) measuring model performance characteristics in unseen data to estimate their external validity Conclusions: We have proposed a ten step process that results in data sets that contain time series features and are suitable for predictive modeling by a number of methods We illustrated the process through an example of cardiac arrest prediction in a pediatric intensive care setting Background Roughly 1-6% of children being cared for in an ICU will experience a cardiac arrest while in the ICU.(1,2) Many of these arrests occur because their vital signs deteriorate to the point where they enter a state of progressive shock.(3-5) These arrests happen despite the fact that they are being continuously monitored by ECG, pulse oximetery, and frequent blood pressure measurements While there are tools that help identify patients in a non-intensive care setting that are at risk of arrest or have deteriorated to the point where they need to transfer to an ICU(621), there are no equivalent tools to identify which patients are likely to arrest in an intensive care setting That is not to say that ICU environments are devoid of useful tools that provide decision support: systems such as VISICU and BioSign/Visensia (22-26) provide an added level of safety to the ICU environment by enabling remote monitoring and providing automated rule checking and high-specificity alerting for deteriorations that occur across multiple channels While these tools are excellent for detecting deteriorations, they still are largely lacking in their ability to predict specific adverse outcomes The goal of this study is to develop a framework for building prediction models that use time series data and can serve as the foundation for tools that can evaluate for specific consequences of a deterioration, with the ultimate goal of augmenting existing systems with the ability answer questions like “Who is most likely to arrest?” in an ICU environment There are over 13,000 tools available to help clinicians interpret the data they are presented(27) Almost all of these tools have been designed so that they can be manually used A tool’s adoption typically depends on a balance between how easy it is to use and what the information content of the tool is(28,29), so tools that are built to be manually used are constrained to a relatively small number of variables in order to achieve adequate simplicity As a result, input variables have typically been restricted to a multivariable data paradigm where each variable is represented by a single value A consequence of this strategy is that useful trend information cannot be incorporated into a model unless it is explicitly encoded as a variable Of course doing this would add complexity to the task, so it is therefore rarely done As healthcare is transitioning from manual processes to electronic ones, it is becoming increasingly easy to automate the processes of data collection and analysis In an automated system, there is no longer a need to remain constrained to a multivariable data paradigm in order to achieve simplicity at the user level Clinical studies using time series analysis has been undertaken in a number of settings(30-41), but thus far has been relatively limited in scope, tending to focus on interpretation of a single analytic method rather than incorporating multiple analytic methods into a more robust modeling paradigm The purpose of this article is to describe a method for developing clinical prediction models based on time-series data elements The model development process that we are presenting is novel to clinical medicine, but the individual steps comprising the process are not Our intention is to provide not only the description of the method, but the theoretical basis of the steps involved We are demonstrating the application of this process in an example of cardiac arrest prediction in a pediatric intensive care unit It is our hope that we describe the steps of the process and their theoretical basis clearly enough that the methods can be extended to other domains where predictions based on time-series data is needed Introduction In order to ensure that the concepts in this article can be understood by clinician and nonclinician alike, we will provide four brief overviews of the core concepts that form the foundation of this article First, we will describe how the growth of data has impacted medicine and some of the strategies that have evolved to manage this growth Second, we will review a few relevant concepts that relate to statistical analysis and modeling, with special focus on multivariable versus time series data paradigms Third, we will specifically discuss clinical prediction models: their utilities, their limitations, and considerations for improvements Finally, we will review the rationale behind selecting cardiac arrest in a pediatric ICU (PICU) as the example to illustrate the process, and we will provide a brief overview of the physiologic principles that serve as the theoretical basis for our prediction model Data in Medicine: Medical care has existed since long before diseases were understood at a scientific level Early medical care was characterized more by art and religion than by science as we know it today(42) The transition of medicine from an art to a science is based on the accumulation of data, and the information, knowledge, and wisdom that has been derived from it While this transition has improved outcomes, there is a side effect of the data: information overload(43-46) Currently, the amount of data in the medical field is so extensive and is growing so fast that is impossible for any single person to utilize it all effectively In order to utilize data, it must be interpreted in context (transforming it into information) and evaluated by the user(47) This process requires substantial cognitive resources and is time consuming In an attempt to address this problem, at least two strategies have been employed: specialization and computerized support(43,48) Specialization allows clinicians to focus their efforts on a narrow field where they become expert in a relatively small group of related diseases In doing so, they reduce their educational burden to a point where they can “afford” the cost of training and staying current in their specialty In fact, some specialties have even reached the point where subspecialization is required in order to stay abreast of the latest trends(49) There is a fundamental limitation to specialization as a means to cope with excessive amounts of data or information: a more robust solution to the problem is needed Ideal properties of the new solution should include: scalability(50) (it can continue to grow indefinitely), flexibility(50,51) (it can be used for a number of purposes), explicit and accurate(51) (it relies on objective parameters), and automaticity(52) (it functions independent of frequent supervision) Computer technology possesses these characteristics, and the field of informatics has been born out of effort to utilize computer based solutions to automate the transformation of data to information in the healthcare setting(53,54) These solutions come in many forms, ranging from aggregating knowledge available on a given disease to informing clinicians when tests or treatments violate parameters deemed to be unsafe(55,56) One of the fundamental goals of this article is to describe a method that can be automated as a computer based solution to help inform clinicians of a patient’s risk of cardiac arrest using trend information that would otherwise require manual interpretation Since clinicians cannot continuously check the risk of cardiac arrest for all patients they are caring for, we are attempting to leverage information from data that would otherwise be left unanalyzed in the current “intermittent check” paradigm Statistical Analysis and Modeling: Of course, medicine is not the only field where data has become so abundant that it is impossible to understand it all Compared to fields such as physics and astronomy, medicine is in a relative state of adolescence When presented with an abundance of data, the first priority is to understand what the data represent This process of gaining an understanding is based on statistical analysis(57-59) Depending on the information needs, data can be analyzed in a number of ways to provide a range of understandings For instance, a univariable analysis(60) of “heart rate” provides an understanding of what the most common heart rate is, the range of heart rates, and how the range is distributed A multivariable analysis(61) that includes “heart rate” as a variable can provide an understanding of how heart rate relates to temperature or blood pressure A time series analysis(62) of “heart rate” can provide an understanding of how the heart rate changes different times of the day The statistical methods for analyzing the data differ fundamentally for time series data since a single variable is represented by multiple values that vary depending on the time they represent Univariable and multivariable statistics, on the other hand, rely on a single value per variable for each case Also, time series data elements are assumed to correlate to adjacent data elements(62), whereas this type of correlation can interfere with univariable and multivariable analysis(63,64) Whereas univariable and multivariable data analysis informs the user of the distribution of a variable across a population and how the variable relates to other variables, time series analysis informs the user of how a variable relates to itself In particular, time series analysis provides two types of information about a variable of interest: trends and seasonality(65) The distinction between the two is that univariable and multivariable analyses aim to describe the static properties of a variable, whereas the aim of a time series analysis is to describe its dynamic properties over time Knowing an airplane is 10 feet off the ground with the nose angled up and is at full throttle are static variables that would suggest a plane is taking off However, knowing that over the last five seconds the elevation was 150 feet off the ground, then 140, then 120, then 90, and then finally 60 feet off the ground changes the interpretation of the multivariable data to suggest that the plane is about to crash The addition of the trend features for the altitude changes the interpretation of the static data about height, pitch and thrust significantly Statistical analysis provides a systematic and standardized process of characterizing data so that it can be understood in the context that it is being analyzed Modeling endeavors also require a systematic approach, but the range of options is more varied than in statistical analysis(66,67) since the products of analyses are often used as “building blocks” for a model It is not uncommon for models to draw on elements from more than one type of analysis in making a prediction One example of this hybrid technique is the time-course approach to microarray analysis(68,69) As an example of this approach, the expression levels of twenty different genes are measured to determine their activity in two classes of cancer If it were to stop here, this would be a basic multivariable model However, the expression levels of these same twenty genes are measured repeatedly under different conditions and at different points in time Under the standard multivariable model that used baseline expression levels of the twenty genes, it is impossible to tell which genes determine cancer class However, by adding the behavior over time in the different nutrient environments, the different classes of cancer can be distinguished from one another This is a well established technique for genomic modeling The technique is based on a paradigm that utilizes time series data elements in a multivariable data format In multivariable statistical analysis, a high degree of correlation between independent variables (known as multicollinearity – an inherent feature of time series data) can invalidate the results of the analysis by invalidating the calculations relating to the analysis of the independent variables as unique components(63,64) However, when modeling is focused on the relationship between the dependent variable and the aggregate of all independent variables (without trying to measure the effects of the independent variables themselves), this multicollinearity is permissible(70) Clinical Prediction Models: For centuries, models have been used to demonstrate our knowledge about the world in which we live They help us share our understandings about the observations we make, and they help us anticipate what is to come In medicine, scoring tools are a class of models that combine multiple data elements, weight them according to their correlation with the outcome of interest, and output a score that can be used in a number of ways Individual scores can be used to make predictions that can help guide treatment decisions and communications with patients and families As an example, medical emergency teams use scoring tools to identify high risk patients that merit transfer to a higher acuity unit(6-9,13-21) Grouping scores allows standardized comparisons between two or more entities by providing a risk-based adjustment to the outcome of interest(10-12,71,72) Almost all clinical models are built on multivariable regression or a regression-like approach that evaluates a number of candidate input features (variables) and measures their individual correlation with the outcome of interest The strength of the correlation is used to assign points for each of the included variables, with more points being assigned for highly correlated variables and for greater deviation from the variable’s normal value Finally, points attributable to each feature are summed together to provide the composite score that provides an estimate of the net effect 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